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Veech groups of flat surfaces with poles
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 57-78.

Les surfaces plates correspondant aux 1-formes méromorphes ou aux différentielles quadratiques contenant des pôles d’ordre au moins deux ont une aire infinie. Nous donnons une classification des groupes apparaissant comme groupes de Veech de surfaces de translation avec pôles. Nous caractérisons les surfaces dont l’orbite sous l’action de GL + (2,) ou SL(2,) est fermée. Enfin, nous déterminons le groupe de Veech d’une surface générique appartenant à une chambre donnée d’une strate.

Flat surfaces that correspond to meromorphic 1-forms with poles or to meromorphic quadratic differentials containing poles of order two and higher have infinite flat area. We classify groups that appear as Veech groups of translation surfaces with poles. We characterize those surfaces such that their GL + (2,)-orbit or their SL(2,)-orbit is closed. Finally, we provide a way to determine the Veech group for a typical infinite surface in any given chamber of a stratum.

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DOI : https://doi.org/10.5802/afst.1623
Mots clés : Translation surface, Veech Group, Flat structure
@article{AFST_2020_6_29_1_57_0,
     author = {Guillaume Tahar},
     title = {Veech groups of flat surfaces with poles},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {57--78},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {1},
     year = {2020},
     doi = {10.5802/afst.1623},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1623/}
}
Guillaume Tahar. Veech groups of flat surfaces with poles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 57-78. doi : 10.5802/afst.1623. https://afst.centre-mersenne.org/articles/10.5802/afst.1623/

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